Dynamic output feedback control of discrete-time switched GRNs with time-varying delays

This paper focuses on the dynamic output feedback (DOF) controller design problem for discrete-time switched genetic regulatory networks (GRNs) with time-varying delays. Firstly, based on the average dwell time method and piecewise Lyapunov–Krasovskii functional, the exponential stability criteria are derived by utilizing a new summation inequality, an extended reciprocally convex matrix inequality and the extension of the property of quadratic convex function. Then, sufficient conditions for a desired DOF controller are obtained such that the resulting closed-loop system is exponentially stable. Moreover, the explicit expressions of all desired controllers are given. Finally, numerical example is provided to verify the effectiveness of the proposed design techniques.